An elementary function is a function built from any combination of $+,-, \cdot, /$ and function composition with polynomial functions, exponential functions, logarithms, and the trigonometric …

Mar 9, 2012 · I suspect the elementary functions are called that simply because they are so simple. This sounds a bit tautological, so let me go on. What classifies as an elementary …

Jan 2, 2016 · Once the elementary functions are defined for real variables, it is a trivial matter to define them for complex variable (just as once we define real numbers in terms of rationals, …

Oct 29, 2017 · It is like an axiom, which is always true. There are many ways to prove that different compound functions are elementary, but $\frac{1}{x}$ is always considered to be …

Oct 27, 2017 · a) The Functions. There are several different ways to define a given function. What we call an elementary function (according to differential algebra) was characterized by …

Aug 22, 2010 · The elementary real-valued functions are not closed under integration. (Elementary function has a precise definition -- see Risch algorithm in Wikipedia). This means …

For questions on elementary functions, functions of one variable built from a finite number of polynomials, exponentials and logarithms through composition and combinations using the …

Mar 22, 2017 · The short answer is that we have differentiation rules for all the elementary functions, and we have differentiation rules for every way we can combine elementary …

Jun 18, 2014 · Liouville used the name "elementary functions" because at the time, that name was still available. You can certainly define a different class of functions. Your only problem is …

Aug 7, 2021 · For indefinite integration of elementary functions by elementary functions, we have Liouville's theorem with Risch algorithm. Solvability of differential equations in certain classes …